Oxford ruined Dack’s Rodney Parade farewell with a 1-0 triumph on the final day of the League Two season with Kemar Roofe smacking a sweetly struck shot past Joe Day in the first half to give his side the lead.
And things got worse for Newport when Michael Flynn was shown red on his 100th appearance for the club for a studs-up challenge on Michael Collins.
Newport’s goal-difference meant a late return to the play-offs was impossible, and the defeat meant they ended the season in ninth position while Oxford’s third straight win gave them a 13th placed finish, and they end the campaign unbeaten in eight matches.
Dack said his emotional farewells to the ground he has called home for four seasons after the final whistle.
And he thinks former England captain Butcher is the right man to lead the Exiles into League One next season.
He said: “Terry is coming in to take this club forward and hopefully he can do that.
“He’ll have a lot of people supporting him and backing him and if he can keep this group of players together then they’re not a million miles away. I feel they’ll get that bit closer next year.
“Terry will have his own ideas but from my perspective this group is not a million miles away.
“Probably we lack a goalscorer; someone to go alongside Aaron O’Connor and get some goals.
“It’s been like my home for four years. The club will move on and I’ll move on but they’ll always have a place in my heart. And I hope I can come back and get a good welcome.
“I just hope the progress goes on now. I’m not one of those who want it to end because I’ve gone.”
Oxford manager Michael Appleton said: “We deserved to win. I thought we were very good in the first half, we played for Newport to make a mistake which we could counter-attack from.
“We created some very good opportunities in the first-half and gave ourselves a platform to work from.
“Sometimes when the opposition go down to 10 men it can be more difficult, we started playing in-front of them instead of around the sides.
“All credit to Newport, the crowd were magnificent, they’ve got great support down here and it made for a great end-of-season game.
“It was an impressive performance and we kept the clean sheet which was important and a bit of magic won the game. Kemar Roofe is full of confidence at the moment and he struck the ball really well.”